code: def lie_heuristic_abaco2_unique_general(match, comp=False):
      r"""
      This heuristic finds if infinitesimals of the form `\eta = f(x)`, `\xi = g(y)`
      without making any assumptions on `h`.
  
      The complete sequence of steps is given in the paper mentioned below.
  
      References
      ==========
      - E.S. Cheb-Terrab, A.D. Roche, Symmetries and First Order
        ODE Patterns, pp. 10 - pp. 12
  
      """
      hx = match["hx"]
      hy = match["hy"]
      func = match["func"]
      x = func.args[0]
      y = match["y"]
      xi = Function("xi")(x, func)
      eta = Function("eta")(x, func)
  
      A = hx.diff(y)
      B = hy.diff(y) + hy**2
      C = hx.diff(x) - hx**2
  
      if not (A and B and C):
          return
  
      Ax = A.diff(x)
      Ay = A.diff(y)
      Axy = Ax.diff(y)
      Axx = Ax.diff(x)
      Ayy = Ay.diff(y)
      D = (
          simplify(2 * Axy + hx * Ay - Ax * hy + (hx * hy + 2 * A) * A)
          * A
          - 3 * Ax * Ay
      )
      if not D:
          E1 = simplify(
              3 * Ax**2 + ((hx**2 + 2 * C) * A - 2 * Axx) * A
          )
          if E1:
              E2 = simplify(
                  (2 * Ayy + (2 * B - hy**2) * A) * A - 3 * Ay**2
              )
              if not E2:
                  E3 = simplify(
                      E1
                      * (
                          (28 * Ax + 4 * hx * A) * A**3
                          - E1 * (hy * A + Ay)
                      )
                      - E1.diff(x) * 8 * A**4
                  )
                  if not E3:
                      etaval = cancel(
                          (
                              4 * A**3 * (Ax - hx * A)
                              + E1 * (hy * A - Ay)
                          )
                          / (S(2) * A * E1)
                      )
                      if x not in etaval:
                          try:
                              etaval = exp(integrate(etaval, y))
                          except NotImplementedError:
                              pass
                          else:
                              xival = -4 * A**3 * etaval / E1
                              if y not in xival:
                                  return [
                                      {
                                          xi: xival,
                                          eta: etaval.subs(y, func),
                                      }
                                  ]
  
      else:
          E1 = simplify(
              (2 * Ayy + (2 * B - hy**2) * A) * A - 3 * Ay**2
          )
          if E1:
              E2 = simplify(
                  4 * A**3 * D
                  - D**2
                  + E1
                  * (
                      (2 * Axx - (hx**2 + 2 * C) * A) * A
                      - 3 * Ax**2
                  )
              )
              if not E2:
                  E3 = simplify(
                      -(A * D) * E1.diff(y)
                      + (
                          (E1.diff(x) - hy * D) * A
                          + 3 * Ay * D
                          + (A * hx - 3 * Ax) * E1
                      )
                      * E1
                  )
                  if not E3:
                      etaval = cancel(
                          ((A * hx - Ax) * E1 - (Ay + A * hy) * D)
                          / (S(2) * A * D)
                      )
                      if x not in etaval:
                          try:
                              etaval = exp(integrate(etaval, y))
                          except NotImplementedError:
                              pass
                          else:
                              xival = -E1 * etaval / D
                              if y not in xival:
                                  return [
                                      {
                                          xi: xival,
                                          eta: etaval.subs(y, func),
                                      }
                                  ]
  
imports: from itertools import islice
  from sympy.core import Add, S, Mul, Pow
  from sympy.core.exprtools import factor_terms
  from sympy.core.function import Function, AppliedUndef, expand
  from sympy.core.relational import Equality, Eq
  from sympy.core.symbol import Symbol, Wild, Dummy, symbols
  from sympy.functions import exp, log
  from sympy.integrals.integrals import integrate
  from sympy.polys import Poly
  from sympy.polys.polytools import cancel, div
  from sympy.simplify import collect, powsimp, separatevars, simplify
  from sympy.solvers import solve
  from sympy.solvers.pde import pdsolve
  from sympy.utilities import numbered_symbols
  from sympy.solvers.deutils import _preprocess, ode_order
  from .ode import checkinfsol
label_desc: Use image node_id 11 for calling a global function with example usage: lie_heuristic_abaco2_unique_general(match, comp) and returns: list, list